After completing the Birthright quest read the letter in the Writing Desk in Gamlen's House. It will come from either the Mercenaries or the Smugglers depending on who you picked in the Prelude. This will lead you to Hubert in the Market of Hightown. Hubert will tell you that something has gone wrong in his mine, which is called The Bone Pit.

Travel to the mine and clear it out. You'll have to clear the mine of Dragonlings and Dragons. Before you go into the mine, head slightly south to find Bearded Beast's remains, this will unlock the Remains of the Outlaw "Bearded Beast" quest. Once you get into the mine, look for a sack on the top level to find Eustice's Pommel and unlock another find and deliver quest.

The final fight with the Mature Dragon isn't easy. Keep weaker fighters away from it and just keep hitting it. After you kill it, collect the Dragon Fang from its corpse, it's required for the Herbalist's Tasks. Once you're done head back to Hubert.

He'll offer to pay you upfront or give you half the mine's interest if you get the workers back, which is the more profitable option. This will start the Get Back to Work quest, which will lead to four other quests in Act 2. Convince the miners to return to complete the Get Back to Work quest.